SOLUTION: The volume of a cone varies jointly as its height, and the square of its radius. If a cone with a height of 8 centimeters and a radius of 2 centimeters has a volume of 33.5 cm3,

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Question 1184202: The volume of a cone varies jointly as its height, and the square of its radius.
If a cone with a height of 8 centimeters and a radius of 2 centimeters has a
volume of 33.5 cm3, what is the volume of a cone with a height of 6 centimeters and a radius of 4 centimeters?
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


A classical mathematical solution....

V=k%28%28h%29%28r%5E2%29%29

(1) Plug in the given values V=33.5, h=8, r=2 and solve for k.
(2) Use that value of k with the new values of h and r to find the new V.

That's simple enough; I leave it to you.

A common sense solution....

The height is changed by a factor of 6/8 = 3/4; that changes the volume by a factor of 3/4.
The radius is changed by a factor of 4/2 = 2; that changes the volume by a factor of 2^2 = 4.

The volume of the second cone is

%2833.5%29%283%2F4%29%284%29=100.5

ANSWER: 100.5 cubic cm